Ministers are considering abolishing a law which requires schools in England to show they promote community cohesion, it has emerged.

Since September 2007, schools have had a legal duty to promote community cohesion and their inspectorate, Ofsted, has had to check that they are doing so.

The requirement – enshrined in the Education and Inspections Act 2006 – was introduced in part to combat fears of a rise in support for the British National Party and Islamophobia.

But the coalition government is now scaling back Ofsted's role and confining its remit to inspecting the quality of leadership in schools, teaching, pupil behaviour and child safety and achievement.

The Department for Education said it would give details of Ofsted's new role "in due course". It would not state whether schools would continue to be inspected according to whether they tackled community cohesion.

However, the chair of the cross-party Commons education committee, Graham Stuart, said Ofsted's remit would no longer include checking schools were promoting community cohesion.

Stuart, Conservative MP for Beverley and Holderness, said this was the right move because it cut bureaucracy and "let schools focus on their core mission". "The best contribution to community cohesion a school can make is providing a good education for all its children," he said.

But former education secretary David Blunkett said abolishing the requirement would be a "deeply retrograde step".

"Withdrawing an emphasis on community cohesion sends entirely the wrong signal, not only in education, but more broadly to society as a whole," Blunkett said.

"An emphasis on community cohesion in schools enables pupils to understand the differences between cultures and backgrounds. It also demonstrated the role of schools as key drivers of functioning, safe and vibrant neighbourhoods."

David Jesson, a professor of educational economics at York University who has researched which schools are best at promoting community cohesion, described proposals to drop the requirement as "disappointing".

He said the creation of "free schools" – new schools founded by parents, teachers and private firms – made it more important to keep the requirement.

"Community cohesion is one of the things at risk with the introduction of free schools. Free schools may have admissions policies that are less responsive to the needs of their communities, which would put community cohesion at risk."

Jesson added that budget cuts would disproportionately affect disadvantaged neighbourhoods where community cohesion was particularly important.

Teaching unions said they would welcome plans to drop the requirement. Russell Hobby, general secretary of the National Association of Head Teachers, said it was "very hard to measure a school's contribution in a tangible tick-box way".

"How can you isolate what a school does [for community cohesion] from what other parts of the community do?"

Brian Lightman, general secretary of the Association of School and College Leaders, said many schools felt that community cohesion was a fundamental part of their ethos. "They don't need bureaucratic requirements on it," he said.

In January, researchers at Bristol University published a study which showed that in some towns and cities in England, children from ethnic minorities are still clustered in just a few schools. The academics used the government's national pupil database to calculate whether white pupils were more or less segregated from their ethnic minority peers in 2008 compared with 2002.

They found that in primary and secondary schools across the country, Bangladeshi and Pakistani pupils are most likely to segregated from their white peers. Oldham, in Greater Manchester, is the most ethnically segregated place in the country, the researchers found.

Last week, the schools minister, Nick Gibb, told the Commons that Ofsted would develop a "new streamlined and refocused inspection framework built around the core areas of pupil achievement, teaching, leadership and behaviour and safety".

The previous government set out guidance for schools on promoting community cohesion. It recommended that teachers helped pupils "value diversity and promote awareness of human rights and the responsibility to uphold and defend them".

A spokesman from the Department for Education said: "Ministers are clear that they want to improve the quality of Ofsted inspections by focusing on four principal areas: the quality of teaching, the effectiveness of leadership, pupils' behaviour and safety, and pupils' achievement. We are working with Ofsted on establishing the new inspection framework and will set this out in detail in due course."